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# hw2-sol - Assignment 2 Section 12.4 Problem 2 Problem 8 The...

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Assignment 2 Section 12.4 Problem 2: Problem 8: The contour diagram in this problem does not represent a linear function. Problem 10: the linear function is: ? = 2 1 2 ? − 2 3 ? Problem 18: A formula for 𝐵 is 𝐵 = 4.2 + 0.9 ? − 120 + 1.6 𝑠 − 8 The formula does not make sense for low weights or speeds. It means 𝐵 > 0 . Problem 22: The formula for this linear function is ? ? , ? = 4 + 2 ? − ? Section 12.5 Problem 2: (a)-(II) (b)-(I) Problem 4: ? 2 + ? 2 + ? 2 = 4 Problem 12: Yes. ? = ? ? , ? = ? 2 + 3 ? 2 Problem 22: since the square root function is non-negative, ? ≥ 0 . Setting ? = 1 − ? 2 − ? 2 and squaring both sides leads to ? 2 + ? 2 + ? 2 = 1 , which is the equation for a sphere of radius 1. The graph of the function includes only those points where ? ≥ 0 , that is, the upper hemisphere of radius 1, centered at the origin. If we take ? ? , ? , ? = ? ? , ? − ? = 1 − ? 2 − ? 2 − ? , then the level surface ? ? , ? , ? = 0 is the surface 𝑆 . Problem 24:

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? − 1 = − ? 2 + ? 2 This is the equation whose graph includes the desired cone. We express this equation as a level surface ? ? , ? , ? = 1 − ? 2 + ? 2 − ? = 0 . Section 12.6 Problem 2: The function 1/( ? 2 + ? 2 ) is continuous on the square. The functions ? 2 and ? 2 are continuous everywhere and so it their sum. The constant function1 is continuous, and thus so is the
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hw2-sol - Assignment 2 Section 12.4 Problem 2 Problem 8 The...

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